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Perpendicular

In elementary geometry, the word perpendicular describes the relationship between two geometric objects that meet at a right angle.
A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if 1 the two lines meet and 2 at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular without specifying an order.
Perpendicularity easily extends to segments and rays. For example, we say a line segment is perpendicular to a line segment if, when each is extended in both directions to form an infinite line, these two resulting lines are perpendicular in the sense above. In symbols, we write to mean line segment AB is perpendicular to line segment CD.
A line is said to be perpendicular to a plane if 1 the line intersects the plane, 2 the line is not completely contained in the plane, and 3 the line is perpendicular to some line in the plane. Note that this definition depends on the definition of perpendicularity between lines.